Conditional Gradient-Type Method. The conditional gradient algorithm, first proposed by [1]}, [2]}, has had a renewed interest in the machine learning and optimization communities in the past decade. We refer the reader to [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, for a partial list of recent works in the deterministic setting. Considering the stochastic convex setup, [9]}, [10]} provided expected oracle complexity results for stochastic conditional gradient algorithm. The complexities were further improved by a sliding procedure in [11]}, based on applying Nesterov's acceleration method in the conditional gradient setup. We also highlight that [12]}, [13]}, [10]} considered variance reduced versions of stochastic conditional gradient algorithm, and provided expected oracle complexities in the non-convex setting. [15]} analyzed the sliding algorithm in the non-convex setting and provided results for the gradient mapping criterion. All of the above works require increasing orders of mini-batches to obtain their oracle complexity results.
